12th grade homeschool curriculum
A full curriculum, starting at your child's level, with lessons connected to their interests and progress you can see.
See the work in 12th grade
Calculus turns a changing system into a question we can measure: what is changing now, and what total does that change produce over time?
- Lesson
- How Fast Is Fast Enough?
- Goal
- Connect a rate of change to an accumulated quantity and use that relationship to make an optimization decision.
- Project
- Give a water tank a deadline
Your parent dashboard
- Today
- Each subject's lesson, and whether it's done
- Grades
- Every submission graded instantly, with written feedback, so you never grade
- Records
- Attendance log and learning summary, ready to export
- Documents
- Transcripts and state-aware compliance drafts, written for you and ready to sign
12th grade scope and sequence
Math13 units · 58 skills
Limits and rates of change6 skills
- Estimate a limit from a table
- Estimate a limit from a graph
- Interpret average and instantaneous rate of change
- Explain when a limit does not exist
- Connect secant and tangent slope ideas
- Use limit language in a context
Derivative models5 skills
- Use a derivative to describe increasing and decreasing behavior
- Interpret derivative units in a context
- Find extrema from a derivative graph
- Compare position, velocity, and acceleration graphs
- Use a tangent-line approximation
Accumulation and integrals4 skills
- Estimate area under a curve with rectangles
- Interpret an integral as accumulated change
- Connect rate graphs to total change
- Compare left, right, and midpoint estimates
Statistical inference5 skills
- Interpret a confidence interval
- Explain a hypothesis test conclusion
- Distinguish statistical significance from practical importance
- Critique sampling and experimental design
- Use simulation to estimate probability
Probability models4 skills
- Use conditional probability in a two-way table
- Apply expected value to a decision
- Model repeated trials with a binomial setting
- Compare independent and dependent events
Vectors and parametric motion4 skills
- Represent a vector by components
- Add vectors graphically and algebraically
- Model two-dimensional motion parametrically
- Interpret speed from a parametric path
Discrete mathematics4 skills
- Use recursion to define a sequence
- Count arrangements with restrictions
- Represent a network with vertices and edges
- Optimize a path in a small network
Financial and decision models4 skills
- Model compound interest with regular contributions
- Compare loan repayment scenarios
- Use sensitivity analysis on a financial model
- Explain model assumptions and risk
Proof and mathematical structure4 skills
- Write a direct proof of a number property
- Use a counterexample to disprove a claim
- Compare inductive and deductive reasoning
- State conditions needed for a theorem
Advanced function connections4 skills
- Analyze a piecewise function at boundaries
- Compare polynomial, exponential, logarithmic, and trigonometric models
- Use transformations to build a complex model
- Justify a modeling choice in writing
Mathematical research modeling4 skills
- Turn a real question into variables and constraints
- Choose data needed for a model
- Validate a model against evidence
- Revise a model after residual or error analysis
AP exam readiness4 skills
- Solve an advanced math mixed item with calculus, statistics, or modeling evidence
- Choose the best method for a timed limit, inference, vector, or decision-model item
- Explain why a grade 12 distractor answer fails
- Write a concise justification for an advanced modeling or inference item
Math capstone6 skills
- Build an original mathematical model
- Defend a calculus or statistics method choice
- Quantify uncertainty in a conclusion
- Critique an alternative model
- Present a college-ready mathematical argument
- Reflect on limits of the chosen model
Reading6 units · 50 skills
Literary reading9 skills
- Identify theme from repeated details
- Explain character motivation
- Analyze how setting shapes conflict
- Interpret figurative language in context
- Compare narrator perspective
- Analyze symbolism
- Trace conflict development
- Compare character arcs
- Compare critical interpretations
Informational reading9 skills
- Identify central idea
- Trace an author's claim
- Distinguish evidence from commentary
- Summarize a section objectively
- Evaluate source credibility
- Identify text structure
- Evaluate evidence relevance
- Analyze author's assumptions
- Evaluate methodological claims in nonfiction
Media and multimodal reading7 skills
- Interpret a chart embedded in an article
- Connect image evidence to a text claim
- Evaluate a caption's relationship to an image
- Compare video and print accounts of an event
- Evaluate scale in an infographic
- Interpret a timeline embedded in text
- Compare headline and article evidence
Vocabulary8 skills
- Use context clues for an unfamiliar word
- Identify connotation
- Distinguish denotation from connotation
- Use word parts to infer meaning
- Infer meaning from analogy
- Use roots and affixes
- Identify figurative versus literal meaning
- Analyze discipline-specific language
Evidence8 skills
- Quote textual evidence accurately
- Paraphrase evidence without changing meaning
- Connect evidence to an inference
- Compare evidence across two texts
- Rank evidence by strength
- Explain why evidence is relevant
- Integrate evidence across genres
- Build an interpretation from scholarly sources
Fluency and text complexity9 skills
- Read grade-level prose with appropriate pacing
- Use punctuation to guide oral phrasing
- Identify sentence complexity in a passage
- Use background knowledge to prepare for a difficult text
- Use paragraph structure to plan reading pace
- Identify unfamiliar syntax before rereading
- Use repeated reading to improve accuracy
- Evaluate text complexity for an independent reading choice
- Use syntax density to explain reading difficulty
English language arts13 units · 60 skills
College-level literature6 skills
- Analyze a complex text through form, context, and ambiguity
- Compare literary movements or traditions
- Evaluate competing interpretations of a text
- Explain intertextual allusion and echo
- Use close reading to support an original interpretation
- Recognize limits of a single interpretive lens
Interpretive lenses4 skills
- Apply a historical lens to a literary passage
- Apply a formal lens to language and structure
- Compare ethical, psychological, or social readings of a text
- Explain what an interpretive lens reveals and hides
Advanced nonfiction and ideas5 skills
- Analyze a philosophical or critical essay for claims and warrants
- Compare two complex arguments about the same issue
- Evaluate how definitions shape argument
- Trace nuance, qualification, and concession in nonfiction
- Summarize a difficult argument accurately
College composition5 skills
- Develop a thesis with stakes and qualification
- Organize a long essay by conceptual movement
- Use evidence from primary and secondary sources
- Write introductions that frame a problem
- Revise paragraphs for cohesion and emphasis
Research argument5 skills
- Design a research question with scholarly stakes
- Build a literature review paragraph
- Integrate source disagreement into an argument
- Use citation to show source relationships
- Revise a claim after evaluating stronger evidence
Creative and rhetorical craft4 skills
- Imitate a mentor text for structure or style
- Use voice deliberately for audience and purpose
- Revise imagery, pacing, and syntax for effect
- Write a reflective commentary on craft choices
Language precision and editing4 skills
- Edit a long essay for style consistency
- Use punctuation for complex academic sentences
- Revise nominalizations and passive constructions deliberately
- Control diction for disciplinary audience
College seminar5 skills
- Lead a seminar using prepared textual evidence
- Ask a question that opens an interpretive problem
- Respond to critique by refining a claim
- Connect multiple speakers' ideas into a shared issue
- Evaluate discussion through evidence and reasoning
Publication and multimodal communication4 skills
- Adapt an argument for a public audience
- Design a multimodal presentation with citation
- Evaluate digital publication credibility and accessibility
- Explain how medium changes audience responsibility
Portfolio revision4 skills
- Select portfolio pieces by evidence of growth
- Write a reflective introduction to a portfolio
- Revise a piece for college-level clarity
- Edit a final portfolio reflection
College reading and writing readiness4 skills
- Annotate a scholarly essay for structure and assumptions
- Write a timed analytical response
- Prepare a conference-style explanation of a paper
- Create a plan for independent reading beyond the course
AP exam readiness4 skills
- Analyze a college-level literature or nonfiction passage under time limits
- Plan a defensible thesis for a senior research or interpretation prompt
- Select textual evidence that best supports a grade 12 line of reasoning
- Revise a senior short response for clarity, precision, and evidence use
ELA capstone6 skills
- Write a college-level literary or nonfiction analysis
- Write a research argument with source conversation
- Present a polished seminar or public talk
- Revise a portfolio for audience and purpose
- Defend an original interpretation under questioning
- Reflect on growth as an independent reader and writer
Science13 units · 57 skills
Advanced scientific research design6 skills
- Turn a broad science question into a testable research design
- Choose variables, controls, and comparison groups
- Plan measurement precision and replication
- Anticipate confounding variables and bias
- Pre-register a claim, method, and analysis plan
- Revise a design after feasibility review
Advanced systems modeling5 skills
- Build a stock-and-flow model for a science system
- Identify feedback loops and delays
- Compare model predictions with data
- Explain assumptions and boundary conditions
- Use sensitivity analysis to test a model
Climate and environmental systems4 skills
- Analyze climate forcing and feedback evidence
- Interpret ocean, atmosphere, and ice data together
- Evaluate land-use and biodiversity tradeoffs
- Compare mitigation and adaptation strategies
Space and planetary science4 skills
- Interpret stellar spectra for composition or motion
- Compare planetary atmospheres and habitability factors
- Use orbital evidence to explain exoplanet detection
- Evaluate claims about space exploration with evidence
Molecular biology and biotechnology4 skills
- Analyze gene regulation at a conceptual level
- Interpret sequencing or protein evidence in a case
- Compare gene therapy, CRISPR, and synthetic biology applications
- Evaluate biosecurity and privacy tradeoffs
Advanced chemistry and materials4 skills
- Connect molecular structure to material properties
- Analyze battery or fuel-cell chemistry evidence
- Compare catalysts by mechanism and performance
- Evaluate a material life-cycle claim
Advanced physics and technology4 skills
- Explain semiconductor behavior conceptually
- Compare sensor technologies by signal and noise
- Analyze energy conversion in a modern device
- Evaluate limits of a physical technology model
Field and community science methods4 skills
- Design a field sampling protocol
- Use geospatial or sensor data responsibly
- Compare citizen-science and controlled-lab evidence
- Explain ethical duties in community data collection
Scientific data analysis4 skills
- Use statistical uncertainty in a science claim
- Compare competing models with residuals or error metrics
- Detect misleading graph choices
- Explain reproducibility and replication limits
Research engineering design4 skills
- Translate research evidence into design criteria
- Prototype a solution under scientific constraints
- Test reliability and failure modes
- Revise a design using quantitative evidence
Science, ethics, and policy4 skills
- Separate scientific claim, value judgment, and policy choice
- Evaluate risk and benefit for affected groups
- Use uncertainty honestly in a recommendation
- Critique a science communication artifact
AP exam readiness4 skills
- Analyze an advanced science research stimulus with method and uncertainty
- Interpret climate, molecular, materials, field, or systems data under time limits
- Choose evidence that supports or weakens an interdisciplinary science claim
- Write a concise advanced science claim-evidence-reasoning response
Science capstone6 skills
- Design an original science investigation or engineering study
- Analyze evidence across at least two scientific domains
- Defend assumptions and uncertainty in a research claim
- Evaluate ethical and societal implications
- Present a college-ready science argument
- Revise the final claim after critique
History12 units · 59 skills
Historical research design6 skills
- Turn a broad historical interest into a researchable question with scope, stakes, and evidence plan
- Build an annotated source base using archives, scholarly books, articles, data, and primary sources
- Distinguish primary evidence, secondary interpretation, historiography, theory, and public memory
- Evaluate source gaps, selection bias, archive power, translation limits, and ethical constraints
- Defend a Grade 12 historical claim about historical research design using conflicting evidence
- Design an annotated bibliography that separates primary sources, scholarly monographs, articles, and reference works
Historiography and interpretive schools5 skills
- Build a historiographical comparison
- Compare political, social, cultural, economic, intellectual, environmental, and microhistorical approaches
- Analyze how historians revise interpretations when evidence, questions, or values change
- Write a literature-review paragraph that identifies debate, evidence base, and intervention
- Compare consensus, Marxist, Annales, postcolonial, feminist, and microhistorical interpretations
Comparative revolutions and state power5 skills
- Compare revolutions with specific evidence across ideology, social base, violence, state collapse, and outcomes
- Analyze American, French, Haitian, Russian, Chinese, Iranian, or anti-colonial revolutions as cases
- Evaluate whether revolutions expand freedom, build stronger states, or produce new exclusions
- Use comparison without flattening local context, chronology, or actor agency
- Defend a Grade 12 historical claim about comparative revolutions and state power using conflicting evidence
Empire, settler colonialism, and decolonization5 skills
- Analyze settler colonialism, extraction empire, indirect rule, law, race, labor, and resistance
- Compare Indigenous sovereignty, land policy, removal, assimilation, and treaty history across cases
- Explain decolonization through nationalism, war, diplomacy, economic dependency, and Cold War pressure
- Evaluate postcolonial memory and reparations debates through evidence and historical responsibility
- Evaluate settler colonialism through land law, migration, labor systems, violence, and memory politics
Political economy and inequality5 skills
- Analyze capitalism, labor, slavery, industrialization, welfare states, neoliberalism, and inequality historically
- Compare taxation, central banking, regulation, public goods, and social insurance as historical choices
- Use economic data carefully by checking measurement, categories, missing people, and interpretive frame
- Explain how political economy links household life, state power, business, empire, and ideology
- Defend a Grade 12 historical claim about political economy and inequality using conflicting evidence
War, genocide, and mass violence4 skills
- Compare total war, civil war, genocide, ethnic cleansing, terrorism, and state repression precisely
- Analyze perpetrator, victim, bystander, rescuer, collaborator, and resistor categories with care
- Evaluate memory and commemoration as evidence
- Explain international law, tribunals, human rights, and prevention debates historically
Environment, technology, and history4 skills
- Analyze environmental history through energy, extraction, agriculture, disease, climate, and infrastructure
- Compare technology as tool, system, labor regime, state project, and cultural force
- Use maps, datasets, images, and material evidence to explain environmental and technological change
- Evaluate claims that technology or environment determines history versus shapes historical possibilities
Public history, memory, and museums6 skills
- Analyze museums, monuments, textbooks, films, podcasts, memorials, and public debates as history work
- Compare commemoration, myth, nostalgia, denial, mourning, repair, and political use of the past
- Design a public-history exhibit label that is accurate, readable, sourced, and ethically framed
- Evaluate contested memory debates without treating all interpretations as equally supported
- Defend a Grade 12 historical claim about public history, memory, and museums using conflicting evidence
- Create a public-history exhibit claim that distinguishes commemoration, interpretation, education, and advocacy
Global Cold War afterlives4 skills
- Compare Cold War afterlives in post-Soviet states, China, Latin America, Africa, and the Middle East
- Analyze development, debt, authoritarianism, human rights, migration, and security after 1991
- Explain how Cold War categories still shape archives, policy memory, and public narratives
- Use regional evidence to avoid U.S.-Soviet-only explanations of global politics
Original research methods5 skills
- Build a citation plan that separates quotation, paraphrase, evidence note, and interpretation
- Create a research matrix linking source, claim, reliability, context, and counterevidence
- Draft a methods note explaining archive/source limits, positionality, and uncertainty
- Revise a claim when new evidence weakens, complicates, or reframes the argument
- Build a source matrix that tracks provenance, genre, claim, limitation, and corroborating evidence
AP exam readiness4 skills
- Write a complex thesis for a comparative or historiographical history prompt
- Use documents to build categories, not summaries, in an advanced historical argument
- Integrate outside evidence and historiography without dropping names decoratively
- Revise a DBQ or LEQ paragraph for sourcing, complexity, and evidence precision
History research capstone6 skills
- Produce a research proposal with question, historiography, source base, method, and stakes
- Defend an original historical claim with primary evidence, secondary scholarship, and counterargument
- Build a public-facing history artifact with source transparency and ethical framing
- Present a capstone argument that explains significance, evidence limits, and unresolved questions
- Defend a Grade 12 historical claim about history research capstone using conflicting evidence
- Defend an original research claim through historiography, primary evidence, method, revision, and presentation
FAQ
- What happens when my child is stuck in a lesson?
- Our Always-On Mentor works beside your senior in every reading and project. They can highlight a calculus step or a line of historiography and ask about it, and it offers help on its own when they seem stuck. During a reading check it answers clarifying questions without giving the answer away.
- How much time does school take each day?
- There is no fixed daily length. Each lesson shows its estimated time, and our Parent Dashboard adds up the day, so you can see the hours against your state's instruction-time rules.
- What are typical 12th grade graduation requirements?
- It depends on your state and your family's graduation plan; there is no single national list. The Parent Dashboard lists every course your teen has finished, so what remains is easy to see.
- Can my senior finish high school with you?
- Yes. Placement starts each remaining course at the right level. Every grade goes onto the transcript we generate.
- How do I finalize my homeschool transcript?
- We generate it from the course and grade records the Parent Dashboard keeps. You sign it as the homeschool administrator.
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